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A193990
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Number of distinct prime factors <= n of binomial(2*n,n).
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3
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0, 1, 1, 1, 2, 2, 2, 3, 2, 1, 3, 2, 3, 3, 3, 3, 4, 5, 5, 6, 5, 4, 4, 4, 4, 4, 3, 5, 7, 5, 5, 6, 7, 6, 6, 5, 5, 6, 5, 5, 6, 6, 7, 7, 7, 7, 8, 9, 8, 8, 7, 6, 8, 8, 6, 6, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 11, 10, 9, 8, 9, 10, 11, 11, 11, 10, 11, 11, 11, 12, 12, 11
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OFFSET
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1,5
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LINKS
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MAPLE
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a := n -> nops(numtheory:-factorset(binomial(2*n, n)) minus select(isprime, {$n+1..2*n})): seq(a(n), n=1..82); # Peter Luschny, Oct 31 2015
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MATHEMATICA
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Table[Length[Select[Transpose[FactorInteger[Binomial[2 n, n]]][[1]], # <= n &]], {n, 100}]
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PROG
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(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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